Banana equivalent dose

A banana equivalent dose (abbreviated BED) is an informal expression of ionizing radiation exposure, intended as a general educational example to indicate the potential dose due to naturally occurring radioactive isotopes by eating one average sized banana. One BED is often taken as 0.1 µSv, however, in practice this dose is not cumulative as the principal radioactive component is excreted to maintain metabolic equilibrium. The BED is only an indicative concept meant to show the existence of very low levels of natural radioactivity within a natural food, and is not a formally adopted dose quantity.

For example, the radiation exposure from consuming a banana is approximately 1% of the average daily exposure to radiation, which is 100 banana equivalent doses (BED). The maximum permitted radiation leakage for a nuclear power plant is equivalent to 2,500 BED (250 μSv), while a chest CT scan delivers 70,000 BED (7 mSv). A lethal dose of radiation treatment is approximately 80,000,000 BED (8 Sv). A person living 10 miles from the Three Mile Island nuclear reactor received 700 BED of exposure to radiation.

Although this whimsical unit is not formally adopted, the use of the word "equivalent" may still cause confusion. Properly, any dose quantity which is a measure of the health effect of radiation on the whole body is known as an "effective" dose. Equivalent doses only relate to specific organs of the body; see article on sievert for naming conventions.

Approximate doses of radiation in sieverts, ranging from trivial to lethal.

The major natural source of radioactivity in plant tissue is potassium: 0.0117% of the naturally-occurring potassium is the unstable isotopepotassium-40 (40K). This isotope decays with a half-life of about 1.25 billion years (4×1016 seconds), and therefore the radioactivity of natural potassium is about 31 Bq/g – meaning that, in one gram of the element, about 31 atoms will decay every second.[2][3] Plants naturally contain other radioactive isotopes, such as carbon-14 (14C), but their contribution to the total activity is much smaller.[citation needed] Since a typical banana contains about half a gram of potassium,[4] it will have an activity of roughly 15 Bq.[5] Although the amount in a single banana is small in environmental and medical terms, the radioactivity from a truckload of bananas is capable of causing a false alarm when passed through a Radiation Portal Monitor used to detect possible smuggling of nuclear material at U.S. ports.[6]

The dose uptake from ingested material is defined as committed dose, and in the case of the overall effect on the human body of the radioactive content of a banana, it will be the "committed effective dose". This is typically given as the net dose over a period of 50 years resulting from the intake of radioactive material.

According to the US Environmental Protection Agency (EPA), isotopically pure potassium-40 will give a committed dose equivalent of 5.02 nanosieverts over 50 years per Becquerel ingested by an average adult.[7] Using this factor, one banana equivalent dose comes out as about 5.02 nSv/Bq × 31 Bq/g × 0.5 g ≈ 78 nanosieverts = 0.078 μSv. In informal publications one often sees this estimate rounded up to 0.1 μSv.[8]

However, the committed dose in the human body due to bananas is not cumulative because the amount of potassium (and therefore of 40K) in the human body is fairly constant because of homeostasis,[9][10] so that any excess absorbed from food is quickly compensated by the elimination of an equal amount.[1][11]

It follows that the additional radiation exposure due to eating a banana lasts only for a few hours after ingestion, i.e. the time it takes for the normal potassium content of the body to be restored by the kidneys. The EPA conversion factor, on the other hand, is based on the mean time needed for the isotopic mix of potassium isotopes in the body to return to the natural ratio after being disturbed by the ingestion of pure 40K; which was assumed by EPA to be 30 days.[9] If the assumed time of residence in the body is reduced by a factor of ten, for example, the estimated equivalent absorbed dose due to the banana will be reduced in the same proportion.

The human body contains about 2.5 grams of potassium per kilogram of body mass,[12] or 175 grams in a 70 kg adult. (Not all of this potassium is 40K, though.) The amount of naturally-occurring potassium decay in humans is therefore less than 175 g × 31 Bq/g ≈ 5400 Bq of radioactive decays, constantly through the person's adult lifetime.

^The activity of one gram of natural potassium is the number of atoms of 40K in it, divided by the average lifetime of a 40K atom in seconds. The number of atoms of 40K in one gram of natural potassium is 40K's mole-fraction (0.000117) times Avogadro's number 6.022×1023 (the number of atoms per mole) divided by the relative atomic mass of potassium (39.0983 grams per mole), namely about 1.80×1018 per gram. As in any exponential decay, the average lifetime is the half-life (3.94 × 1016 seconds) divided by the natural logarithm of 2, or about 5.684×1016 seconds.

^ abU. S. Environmental Protection Agency (1999), Federal Guidance Report 13, page 16: "For example, the ingestion coefficient risk for 40K would not be appropriate for an application to ingestion of 40K in conjunction with an elevated intake of natural potassiumm. This is because the biokinetic model for potassium used in this document represents the relatively slow removal of potassium (biological half-time 30 days) that is estimated to occur for typical intakes of potassium, whereas an elevated intake of potassium would result in excretion of a nearly equal mass of natural potassium, and hence of 40K, over a short period."